I have been told that ID protection actually is whois protection when register domain. However,there is "privacy protection" in domain control panel. I wonder whether the said ID protection is equivalent to privacy protection .

I'd guess so, but you'll want to check with whatever control panel you're using. I've heard the terms interchanged, but it's always best to ask whoever you're buying it from, if it's the same thing, or something different just for them.